In his sixth start since replacing the injured Drew Bledsoe, Brady threw touchdown passes of four, 15 and 44 yards. He went 21 of 31 for 250 yards, completing passes to eight different receivers.
Brady, who was intercepted four times in the fourth quarter of last Sunday's loss at Denver, improved to 4-2 as the club's starter. Bledsoe lost his two starts before suffering a chest injury against the New York Jets on Sept. 23.
Antowain Smith rushed for 117 yards and Adam Vinatieri added a 48-yard field goal for the Patriots (4-4), who had lost their last three meetings against Atlanta by a combined score of 105-27.
It was a rough afternoon for Falcons oft-injured quarterback Chris Chandler, who left the contest late in the third quarter with a rib injury. He went eight of 20 for 95 yards with one touchdown and an interception before being replaced by Michael Vick.
Vick, the the top pick in April's draft, also struggled while going two of nine for 56 yards.
Maurice Smith rushed for 84 yards for Atlanta (3-4), which lost for the third time in its last four games.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys